LMFDB - Embedded newform 656.2.bs.d.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(33,656)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("656.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.bs (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.3
Character	$\chi$	$=$	656.33
Dual form			656.2.bs.d.497.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.02366 - 2.02366i) q^{3} +(0.110420 - 0.0358775i) q^{5} +(0.422339 - 2.66654i) q^{7} -5.19040i q^{9} +O(q^{10})$	\(q+(2.02366 - 2.02366i) q^{3} +(0.110420 - 0.0358775i) q^{5} +(0.422339 - 2.66654i) q^{7} -5.19040i q^{9} +(1.53663 + 3.01580i) q^{11} +(-1.03889 + 0.164544i) q^{13} +(0.150848 - 0.296056i) q^{15} +(3.25831 - 1.66019i) q^{17} +(2.25168 + 0.356630i) q^{19} +(-4.54151 - 6.25085i) q^{21} +(-6.06568 - 4.40698i) q^{23} +(-4.03418 + 2.93100i) q^{25} +(-4.43263 - 4.43263i) q^{27} +(1.31408 + 0.669558i) q^{29} +(0.964816 - 2.96940i) q^{31} +(9.21257 + 2.99335i) q^{33} +(-0.0490344 - 0.309591i) q^{35} +(-0.348766 - 1.07339i) q^{37} +(-1.76938 + 2.43534i) q^{39} +(-1.32339 + 6.26487i) q^{41} +(-0.583672 + 0.803355i) q^{43} +(-0.186219 - 0.573122i) q^{45} +(1.73020 + 10.9241i) q^{47} +(-0.274693 - 0.0892531i) q^{49} +(3.23405 - 9.95337i) q^{51} +(0.482987 + 0.246094i) q^{53} +(0.277873 + 0.277873i) q^{55} +(5.27833 - 3.83493i) q^{57} +(1.57246 + 1.14246i) q^{59} +(-5.95937 - 8.20238i) q^{61} +(-13.8404 - 2.19211i) q^{63} +(-0.108810 + 0.0554416i) q^{65} +(6.02949 - 11.8335i) q^{67} +(-21.1931 + 3.35666i) q^{69} +(4.28484 + 8.40947i) q^{71} +10.9108i q^{73} +(-2.23245 + 14.0952i) q^{75} +(8.69075 - 2.82380i) q^{77} +(-7.58864 + 7.58864i) q^{79} -2.36906 q^{81} +0.635212 q^{83} +(0.300218 - 0.300218i) q^{85} +(4.01421 - 1.30430i) q^{87} +(0.753161 - 4.75527i) q^{89} +2.83974i q^{91} +(-4.05659 - 7.96151i) q^{93} +(0.261424 - 0.0414055i) q^{95} +(-1.25412 + 2.46135i) q^{97} +(15.6532 - 7.97572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.02366	−	2.02366i	1.16836	−	1.16836i	0.185767	−	0.982594i	$-0.440523\pi$
$3$	2.02366	−	2.02366i	1.16836	−	1.16836i	0.982594	−	0.185767i	$-0.0594769\pi$
$4$		0			0
$5$	0.110420	−	0.0358775i	0.0493811	−	0.0160449i	−0.284222	−	0.958758i	$-0.591735\pi$
$5$	0.110420	−	0.0358775i	0.0493811	−	0.0160449i	0.333603	+	0.942714i	$0.391735\pi$
$6$		0			0
$7$	0.422339	−	2.66654i	0.159629	−	1.00786i	−0.769646	−	0.638471i	$-0.779567\pi$
$7$	0.422339	−	2.66654i	0.159629	−	1.00786i	0.929275	−	0.369388i	$-0.120433\pi$
$8$		0			0
$9$		−	5.19040i		−	1.73013i
$10$		0			0
$11$	1.53663	+	3.01580i	0.463311	+	0.909299i	0.997936	+	0.0642096i	$0.0204526\pi$
$11$	1.53663	+	3.01580i	0.463311	+	0.909299i	−0.534626	+	0.845089i	$0.679547\pi$
$12$		0			0
$13$	−1.03889	+	0.164544i	−0.288136	+	0.0456362i	−0.298829	−	0.954307i	$-0.596596\pi$
$13$	−1.03889	+	0.164544i	−0.288136	+	0.0456362i	0.0106934	+	0.999943i	$0.496596\pi$
$14$		0			0
$15$	0.150848	−	0.296056i	0.0389488	−	0.0764412i
$16$		0			0
$17$	3.25831	−	1.66019i	0.790256	−	0.402655i	−0.0117807	−	0.999931i	$-0.503750\pi$
$17$	3.25831	−	1.66019i	0.790256	−	0.402655i	0.802036	+	0.597275i	$0.203750\pi$
$18$		0			0
$19$	2.25168	+	0.356630i	0.516570	+	0.0818166i	0.409276	−	0.912411i	$-0.365781\pi$
$19$	2.25168	+	0.356630i	0.516570	+	0.0818166i	0.107294	+	0.994227i	$0.465781\pi$
$20$		0			0
$21$	−4.54151	−	6.25085i	−0.991038	−	1.36405i
$22$		0			0
$23$	−6.06568	−	4.40698i	−1.26478	−	0.918918i	−0.265800	−	0.964028i	$-0.585636\pi$
$23$	−6.06568	−	4.40698i	−1.26478	−	0.918918i	−0.998982	+	0.0451098i	$0.985636\pi$
$24$		0			0
$25$	−4.03418	+	2.93100i	−0.806836	+	0.586201i
$26$		0			0
$27$	−4.43263	−	4.43263i	−0.853060	−	0.853060i
$28$		0			0
$29$	1.31408	+	0.669558i	0.244019	+	0.124334i	0.571723	−	0.820446i	$-0.306275\pi$
$29$	1.31408	+	0.669558i	0.244019	+	0.124334i	−0.327705	+	0.944780i	$0.606275\pi$
$30$		0			0
$31$	0.964816	−	2.96940i	0.173286	−	0.533320i	−0.826265	−	0.563282i	$-0.809539\pi$
$31$	0.964816	−	2.96940i	0.173286	−	0.533320i	0.999551	+	0.0299620i	$0.00953862\pi$
$32$		0			0
$33$	9.21257	+	2.99335i	1.60370	+	0.521075i
$34$		0			0
$35$	−0.0490344	−	0.309591i	−0.00828833	−	0.0523305i
$36$		0			0
$37$	−0.348766	−	1.07339i	−0.0573368	−	0.176465i	0.918286	−	0.395917i	$-0.129573\pi$
$37$	−0.348766	−	1.07339i	−0.0573368	−	0.176465i	−0.975623	+	0.219452i	$0.929573\pi$
$38$		0			0
$39$	−1.76938	+	2.43534i	−0.283327	+	0.389966i
$40$		0			0
$41$	−1.32339	+	6.26487i	−0.206678	+	0.978409i
$41$	−1.32339	+	6.26487i	−0.206678	+	0.978409i
$42$		0			0
$43$	−0.583672	+	0.803355i	−0.0890091	+	0.122511i	−0.851199	−	0.524843i	$-0.824124\pi$
$43$	−0.583672	+	0.803355i	−0.0890091	+	0.122511i	0.762190	+	0.647353i	$0.224124\pi$
$44$		0			0
$45$	−0.186219	−	0.573122i	−0.0277598	−	0.0854360i
$46$		0			0
$47$	1.73020	+	10.9241i	0.252376	+	1.59344i	0.709939	+	0.704263i	$0.248722\pi$
$47$	1.73020	+	10.9241i	0.252376	+	1.59344i	−0.457563	+	0.889177i	$0.651278\pi$
$48$		0			0
$49$	−0.274693	−	0.0892531i	−0.0392418	−	0.0127504i
$50$		0			0
$51$	3.23405	−	9.95337i	0.452857	−	1.39375i
$52$		0			0
$53$	0.482987	+	0.246094i	0.0663434	+	0.0338036i	0.486847	−	0.873487i	$-0.338147\pi$
$53$	0.482987	+	0.246094i	0.0663434	+	0.0338036i	−0.420504	+	0.907291i	$0.638147\pi$
$54$		0			0
$55$	0.277873	+	0.277873i	0.0374684	+	0.0374684i
$56$		0			0
$57$	5.27833	−	3.83493i	0.699131	−	0.507949i
$58$		0			0
$59$	1.57246	+	1.14246i	0.204717	+	0.148735i	0.685420	−	0.728148i	$-0.259619\pi$
$59$	1.57246	+	1.14246i	0.204717	+	0.148735i	−0.480703	+	0.876883i	$0.659619\pi$
$60$		0			0
$61$	−5.95937	−	8.20238i	−0.763020	−	1.05021i	−0.996957	−	0.0779548i	$-0.975161\pi$
$61$	−5.95937	−	8.20238i	−0.763020	−	1.05021i	0.233937	−	0.972252i	$-0.424839\pi$
$62$		0			0
$63$	−13.8404	−	2.19211i	−1.74373	−	0.276180i
$64$		0			0
$65$	−0.108810	+	0.0554416i	−0.0134962	+	0.00687668i
$66$		0			0
$67$	6.02949	−	11.8335i	0.736619	−	1.44570i	−0.152635	−	0.988283i	$-0.548776\pi$
$67$	6.02949	−	11.8335i	0.736619	−	1.44570i	0.889254	−	0.457414i	$-0.151224\pi$
$68$		0			0
$69$	−21.1931	+	3.35666i	−2.55135	+	0.404094i
$70$		0			0
$71$	4.28484	+	8.40947i	0.508517	+	0.998021i	0.992419	+	0.122899i	$0.0392190\pi$
$71$	4.28484	+	8.40947i	0.508517	+	0.998021i	−0.483902	+	0.875122i	$0.660781\pi$
$72$		0			0
$73$			10.9108i			1.27702i	0.769615	+	0.638508i	$0.220448\pi$
$73$			10.9108i			1.27702i	−0.769615	+	0.638508i	$0.779552\pi$
$74$		0			0
$75$	−2.23245	+	14.0952i	−0.257782	+	1.62757i
$76$		0			0
$77$	8.69075	−	2.82380i	0.990403	−	0.321801i
$78$		0			0
$79$	−7.58864	+	7.58864i	−0.853789	+	0.853789i	−0.990597	−	0.136809i	$-0.956315\pi$
$79$	−7.58864	+	7.58864i	−0.853789	+	0.853789i	0.136809	+	0.990597i	$0.456315\pi$
$80$		0			0
$81$	−2.36906			−0.263229
$82$		0			0
$83$	0.635212			0.0697236			0.0348618	−	0.999392i	$-0.488901\pi$
$83$	0.635212			0.0697236			0.0348618	+	0.999392i	$0.488901\pi$
$84$		0			0
$85$	0.300218	−	0.300218i	0.0325632	−	0.0325632i
$86$		0			0
$87$	4.01421	−	1.30430i	0.430369	−	0.139835i
$88$		0			0
$89$	0.753161	−	4.75527i	0.0798350	−	0.504058i	−0.915074	−	0.403285i	$-0.867868\pi$
$89$	0.753161	−	4.75527i	0.0798350	−	0.504058i	0.994909	−	0.100773i	$-0.0321316\pi$
$90$		0			0
$91$			2.83974i			0.297685i
$92$		0			0
$93$	−4.05659	−	7.96151i	−0.420649	−	0.825570i
$94$		0			0
$95$	0.261424	−	0.0414055i	0.0268216	−	0.00424812i
$96$		0			0
$97$	−1.25412	+	2.46135i	−0.127337	+	0.249913i	−0.945869	−	0.324548i	$-0.894788\pi$
$97$	−1.25412	+	2.46135i	−0.127337	+	0.249913i	0.818533	+	0.574460i	$0.194788\pi$
$98$		0			0
$99$	15.6532	−	7.97572i	1.57321	−	0.801590i
$100$		0			0
$101$	9.34392	+	1.47993i	0.929755	+	0.147259i	0.602901	−	0.797816i	$-0.294012\pi$
$101$	9.34392	+	1.47993i	0.929755	+	0.147259i	0.326854	+	0.945075i	$0.394012\pi$
$102$		0			0
$103$	−3.69313	−	5.08316i	−0.363895	−	0.500858i	0.587334	−	0.809345i	$-0.300178\pi$
$103$	−3.69313	−	5.08316i	−0.363895	−	0.500858i	−0.951229	+	0.308486i	$0.900178\pi$
$104$		0			0
$105$	−0.725737	−	0.527278i	−0.0708246	−	0.0514571i
$106$		0			0
$107$	11.1143	−	8.07504i	1.07446	−	0.780644i	0.0977545	−	0.995211i	$-0.468834\pi$
$107$	11.1143	−	8.07504i	1.07446	−	0.780644i	0.976709	+	0.214567i	$0.0688340\pi$
$108$		0			0
$109$	10.4978	+	10.4978i	1.00551	+	1.00551i	0.999985	+	0.00552465i	$0.00175856\pi$
$109$	10.4978	+	10.4978i	1.00551	+	1.00551i	0.00552465	+	0.999985i	$0.498241\pi$
$110$		0			0
$111$	−2.87796	−	1.46640i	−0.273164	−	0.139184i
$112$		0			0
$113$	2.45600	−	7.55880i	0.231041	−	0.711073i	−0.766580	−	0.642148i	$-0.778043\pi$
$113$	2.45600	−	7.55880i	0.231041	−	0.711073i	0.997622	−	0.0689242i	$-0.0219567\pi$
$114$		0			0
$115$	−0.827882	−	0.268995i	−0.0772004	−	0.0250839i
$116$		0			0
$117$	0.854048	+	5.39225i	0.0789568	+	0.498514i
$118$		0			0
$119$	−3.05086	−	9.38959i	−0.279672	−	0.860742i
$120$		0			0
$121$	−0.268199	+	0.369145i	−0.0243818	+	0.0335586i
$122$		0			0
$123$	9.99989	+	15.3561i	0.901660	+	1.38461i
$124$		0			0
$125$	−0.681511	+	0.938019i	−0.0609562	+	0.0838990i
$126$		0			0
$127$	2.50455	+	7.70820i	0.222243	+	0.683993i	0.998560	+	0.0536500i	$0.0170855\pi$
$127$	2.50455	+	7.70820i	0.222243	+	0.683993i	−0.776317	+	0.630343i	$0.782914\pi$
$128$		0			0
$129$	0.444565	+	2.80687i	0.0391417	+	0.247131i
$130$		0			0
$131$	10.8285	+	3.51838i	0.946087	+	0.307402i	0.741125	−	0.671368i	$-0.234293\pi$
$131$	10.8285	+	3.51838i	0.946087	+	0.307402i	0.204962	+	0.978770i	$0.434293\pi$
$132$		0			0
$133$	1.90194	−	5.85357i	0.164919	−	0.507569i
$134$		0			0
$135$	−0.648481	−	0.330417i	−0.0558123	−	0.0284378i
$136$		0			0
$137$	4.26765	+	4.26765i	0.364610	+	0.364610i	0.865507	−	0.500897i	$-0.166996\pi$
$137$	4.26765	+	4.26765i	0.364610	+	0.364610i	−0.500897	+	0.865507i	$0.666996\pi$
$138$		0			0
$139$	−14.2798	+	10.3749i	−1.21120	+	0.879987i	−0.995339	−	0.0964369i	$-0.969255\pi$
$139$	−14.2798	+	10.3749i	−1.21120	+	0.879987i	−0.215860	+	0.976424i	$0.569255\pi$
$140$		0			0
$141$	25.6080	+	18.6053i	2.15658	+	1.56685i
$142$		0			0
$143$	−2.09262	−	2.88024i	−0.174993	−	0.240858i
$144$		0			0
$145$	0.169122	+	0.0267864i	0.0140449	+	0.00222449i
$146$		0			0
$147$	−0.736503	+	0.375267i	−0.0607458	+	0.0309515i
$148$		0			0
$149$	0.491547	−	0.964715i	0.0402691	−	0.0790326i	−0.869995	−	0.493060i	$-0.835878\pi$
$149$	0.491547	−	0.964715i	0.0402691	−	0.0790326i	0.910264	+	0.414028i	$0.135878\pi$
$150$		0			0
$151$	−12.9796	+	2.05577i	−1.05626	+	0.167296i	−0.660324	−	0.750980i	$-0.729581\pi$
$151$	−12.9796	+	2.05577i	−1.05626	+	0.167296i	−0.395940	+	0.918276i	$0.629581\pi$
$152$		0			0
$153$	−8.61706	−	16.9119i	−0.696648	−	1.36725i
$154$		0			0
$155$		−	0.362495i		−	0.0291163i
$156$		0			0
$157$	−2.56436	+	16.1907i	−0.204658	+	1.29216i	0.644737	+	0.764404i	$0.276967\pi$
$157$	−2.56436	+	16.1907i	−0.204658	+	1.29216i	−0.849396	+	0.527757i	$0.823033\pi$
$158$		0			0
$159$	1.47541	−	0.479391i	0.117008	−	0.0380181i
$160$		0			0
$161$	−14.3132	+	14.3132i	−1.12804	+	1.12804i
$162$		0			0
$163$	−14.6327			−1.14612			−0.573059	−	0.819514i	$-0.694243\pi$
$163$	−14.6327			−1.14612			−0.573059	+	0.819514i	$0.694243\pi$
$164$		0			0
$165$	1.12464			0.0875533
$166$		0			0
$167$	8.21554	−	8.21554i	0.635738	−	0.635738i	−0.313764	−	0.949501i	$-0.601590\pi$
$167$	8.21554	−	8.21554i	0.635738	−	0.635738i	0.949501	+	0.313764i	$0.101590\pi$
$168$		0			0
$169$	−11.3115	+	3.67534i	−0.870117	+	0.282718i
$170$		0			0
$171$	1.85106	−	11.6871i	0.141554	−	0.893735i
$172$		0			0
$173$		−	2.01872i		−	0.153480i	−0.997051	−	0.0767400i	$-0.975549\pi$
$173$		−	2.01872i		−	0.153480i	0.997051	−	0.0767400i	$-0.0244512\pi$
$174$		0			0
$175$	6.11186	+	11.9952i	0.462013	+	0.906752i
$176$		0			0
$177$	5.49407	−	0.870175i	0.412960	−	0.0654064i
$178$		0			0
$179$	−8.10933	+	15.9155i	−0.606120	+	1.18958i	0.360355	+	0.932815i	$0.382656\pi$
$179$	−8.10933	+	15.9155i	−0.606120	+	1.18958i	−0.966475	+	0.256762i	$0.917344\pi$
$180$		0			0
$181$	−1.57724	+	0.803644i	−0.117235	+	0.0597344i	−0.511625	−	0.859209i	$-0.670956\pi$
$181$	−1.57724	+	0.803644i	−0.117235	+	0.0597344i	0.394389	+	0.918943i	$0.370956\pi$
$182$		0			0
$183$	−28.6586	−	4.53907i	−2.11850	−	0.335538i
$184$		0			0
$185$	−0.0770212	−	0.106011i	−0.00566271	−	0.00779406i
$186$		0			0
$187$	10.0136	+	7.27532i	0.732268	+	0.532024i
$188$		0			0
$189$	−13.6919	+	9.94773i	−0.995937	+	0.723591i
$190$		0			0
$191$	3.86040	+	3.86040i	0.279329	+	0.279329i	0.832841	−	0.553512i	$-0.186713\pi$
$191$	3.86040	+	3.86040i	0.279329	+	0.279329i	−0.553512	+	0.832841i	$0.686713\pi$
$192$		0			0
$193$	−5.84374	−	2.97753i	−0.420641	−	0.214328i	0.230841	−	0.972992i	$-0.425852\pi$
$193$	−5.84374	−	2.97753i	−0.420641	−	0.214328i	−0.651482	+	0.758664i	$0.725852\pi$
$194$		0			0
$195$	−0.108000	+	0.332390i	−0.00773404	+	0.0238029i
$196$		0			0
$197$	−4.06150	−	1.31966i	−0.289370	−	0.0940220i	0.160735	−	0.986998i	$-0.448613\pi$
$197$	−4.06150	−	1.31966i	−0.289370	−	0.0940220i	−0.450105	+	0.892976i	$0.648613\pi$
$198$		0			0
$199$	2.50210	+	15.7976i	0.177369	+	1.11986i	0.902321	+	0.431064i	$0.141862\pi$
$199$	2.50210	+	15.7976i	0.177369	+	1.11986i	−0.724952	+	0.688799i	$0.758138\pi$
$200$		0			0
$201$	−11.7454	−	36.1487i	−0.828458	−	2.54973i
$202$		0			0
$203$	2.34039	−	3.22128i	0.164263	−	0.226089i
$204$		0			0
$205$	0.0786403	+	0.739245i	0.00549248	+	0.0516311i
$206$		0			0
$207$	−22.8740	+	31.4833i	−1.58985	+	2.18824i
$208$		0			0
$209$	2.38446	+	7.33862i	0.164937	+	0.507623i
$210$		0			0
$211$	−3.90790	−	24.6735i	−0.269031	−	1.69859i	−0.638722	−	0.769438i	$-0.720536\pi$
$211$	−3.90790	−	24.6735i	−0.269031	−	1.69859i	0.369691	−	0.929155i	$-0.379464\pi$
$212$		0			0
$213$	25.6890	+	8.34685i	1.76018	+	0.571917i
$214$		0			0
$215$	−0.0356264	+	0.109647i	−0.00242970	+	0.00747785i
$216$		0			0
$217$	−7.51055	−	3.82682i	−0.509849	−	0.259781i
$218$		0			0
$219$	22.0798	+	22.0798i	1.49202	+	1.49202i
$220$		0			0
$221$	−3.11184	+	2.26089i	−0.209325	+	0.152084i
$222$		0			0
$223$	2.68513	+	1.95086i	0.179809	+	0.130639i	0.674049	−	0.738686i	$-0.264554\pi$
$223$	2.68513	+	1.95086i	0.179809	+	0.130639i	−0.494240	+	0.869326i	$0.664554\pi$
$224$		0			0
$225$	15.2131	+	20.9390i	1.01421	+	1.39593i
$226$		0			0
$227$	7.61270	+	1.20573i	0.505272	+	0.0800273i	0.403867	−	0.914818i	$-0.367666\pi$
$227$	7.61270	+	1.20573i	0.505272	+	0.0800273i	0.101406	+	0.994845i	$0.467666\pi$
$228$		0			0
$229$	4.43150	−	2.25796i	0.292842	−	0.149210i	−0.301398	−	0.953499i	$-0.597453\pi$
$229$	4.43150	−	2.25796i	0.292842	−	0.149210i	0.594240	+	0.804288i	$0.297453\pi$
$230$		0			0
$231$	11.8727	−	23.3015i	0.781168	−	1.53313i
$232$		0			0
$233$	−10.5733	+	1.67465i	−0.692680	+	0.109710i	−0.492841	−	0.870119i	$-0.664042\pi$
$233$	−10.5733	+	1.67465i	−0.692680	+	0.109710i	−0.199838	+	0.979829i	$0.564042\pi$
$234$		0			0
$235$	0.582977	+	1.14416i	0.0380292	+	0.0746366i
$236$		0			0
$237$			30.7137i			1.99507i
$238$		0			0
$239$	1.44605	−	9.13003i	0.0935375	−	0.590572i	−0.895746	−	0.444566i	$-0.853358\pi$
$239$	1.44605	−	9.13003i	0.0935375	−	0.590572i	0.989284	−	0.146006i	$-0.0466420\pi$
$240$		0			0
$241$	−26.9539	+	8.75786i	−1.73626	+	0.564144i	−0.994330	−	0.106339i	$-0.966087\pi$
$241$	−26.9539	+	8.75786i	−1.73626	+	0.564144i	−0.741925	+	0.670482i	$0.766087\pi$
$242$		0			0
$243$	8.50371	−	8.50371i	0.545513	−	0.545513i
$244$		0			0
$245$	−0.0335337			−0.00214239
$246$		0			0
$247$	−2.39792			−0.152576
$248$		0			0
$249$	1.28545	−	1.28545i	0.0814623	−	0.0814623i
$250$		0			0
$251$	−6.28383	+	2.04174i	−0.396632	+	0.128874i	−0.500540	−	0.865713i	$-0.666865\pi$
$251$	−6.28383	+	2.04174i	−0.396632	+	0.128874i	0.103908	+	0.994587i	$0.466865\pi$
$252$		0			0
$253$	3.96987	−	25.0648i	0.249584	−	1.57581i
$254$		0			0
$255$		−	1.21508i		−	0.0760910i
$256$		0			0
$257$	−1.99593	−	3.91722i	−0.124502	−	0.244350i	0.820339	−	0.571877i	$-0.193785\pi$
$257$	−1.99593	−	3.91722i	−0.124502	−	0.244350i	−0.944842	+	0.327527i	$0.893785\pi$
$258$		0			0
$259$	−3.00954	+	0.476665i	−0.187004	+	0.0296185i
$260$		0			0
$261$	3.47528	−	6.82061i	0.215114	−	0.422185i
$262$		0			0
$263$	11.1561	−	5.68432i	0.687915	−	0.350510i	−0.0748417	−	0.997195i	$-0.523845\pi$
$263$	11.1561	−	5.68432i	0.687915	−	0.350510i	0.762757	+	0.646685i	$0.223845\pi$
$264$		0			0
$265$	0.0621605	+	0.00984525i	0.00381849	+	0.000604789i
$266$		0			0
$267$	−8.09892	−	11.1472i	−0.495646	−	0.682198i
$268$		0			0
$269$	−2.86327	−	2.08029i	−0.174577	−	0.126838i	0.497066	−	0.867713i	$-0.334411\pi$
$269$	−2.86327	−	2.08029i	−0.174577	−	0.126838i	−0.671642	+	0.740875i	$0.734411\pi$
$270$		0			0
$271$	−3.09632	+	2.24961i	−0.188088	+	0.136654i	−0.677845	−	0.735205i	$-0.737086\pi$
$271$	−3.09632	+	2.24961i	−0.188088	+	0.136654i	0.489756	+	0.871859i	$0.337086\pi$
$272$		0			0
$273$	5.74666	+	5.74666i	0.347804	+	0.347804i
$274$		0			0
$275$	−15.0384	−	7.66243i	−0.906847	−	0.462062i
$276$		0			0
$277$	9.27253	−	28.5379i	0.557132	−	1.71468i	−0.133112	−	0.991101i	$-0.542497\pi$
$277$	9.27253	−	28.5379i	0.557132	−	1.71468i	0.690244	−	0.723576i	$-0.257503\pi$
$278$		0			0
$279$	−15.4124	−	5.00778i	−0.922714	−	0.299808i
$280$		0			0
$281$	0.860451	+	5.43268i	0.0513302	+	0.324086i	0.999970	+	0.00772841i	$0.00246005\pi$
$281$	0.860451	+	5.43268i	0.0513302	+	0.324086i	−0.948640	+	0.316358i	$0.897540\pi$
$282$		0			0
$283$	−9.37505	−	28.8534i	−0.557289	−	1.71516i	−0.689822	−	0.723979i	$-0.742311\pi$
$283$	−9.37505	−	28.8534i	−0.557289	−	1.71516i	0.132533	−	0.991179i	$-0.457689\pi$
$284$		0			0
$285$	0.445243	−	0.612824i	0.0263739	−	0.0363006i
$286$		0			0
$287$	16.1466	+	6.17477i	0.953106	+	0.364485i
$288$		0			0
$289$	−2.13201	+	2.93447i	−0.125413	+	0.172616i
$290$		0			0
$291$	2.44303	+	7.51886i	0.143213	+	0.440763i
$292$		0			0
$293$	−3.14362	−	19.8480i	−0.183652	−	1.15953i	−0.891450	−	0.453119i	$-0.850311\pi$
$293$	−3.14362	−	19.8480i	−0.183652	−	1.15953i	0.707798	−	0.706415i	$-0.249689\pi$
$294$		0			0
$295$	0.214619	+	0.0697339i	0.0124956	+	0.00406006i
$296$		0			0
$297$	6.55663	−	20.1792i	0.380454	−	1.17092i
$298$		0			0
$299$	7.02671	+	3.58029i	0.406365	+	0.207053i
$300$		0			0
$301$	1.89568	+	1.89568i	0.109265	+	0.109265i
$302$		0			0
$303$	21.9038	−	15.9140i	1.25834	−	0.914237i
$304$		0			0
$305$	−0.952313	−	0.691896i	−0.0545293	−	0.0396178i
$306$		0			0
$307$	−0.132775	−	0.182749i	−0.00757787	−	0.0104300i	0.805211	−	0.592988i	$-0.202052\pi$
$307$	−0.132775	−	0.182749i	−0.00757787	−	0.0104300i	−0.812789	+	0.582558i	$0.802052\pi$
$308$		0			0
$309$	−17.7602	−	2.81294i	−1.01034	−	0.160023i
$310$		0			0
$311$	−12.9469	+	6.59679i	−0.734153	+	0.374070i	−0.780750	−	0.624844i	$-0.785163\pi$
$311$	−12.9469	+	6.59679i	−0.734153	+	0.374070i	0.0465963	+	0.998914i	$0.485163\pi$
$312$		0			0
$313$	3.71571	−	7.29249i	0.210024	−	0.412196i	−0.761831	−	0.647776i	$-0.775699\pi$
$313$	3.71571	−	7.29249i	0.210024	−	0.412196i	0.971855	+	0.235581i	$0.0756992\pi$
$314$		0			0
$315$	−1.60690	+	0.254508i	−0.0905387	+	0.0143399i
$316$		0			0
$317$	4.35992	+	8.55683i	0.244878	+	0.480600i	0.980430	−	0.196868i	$-0.0630772\pi$
$317$	4.35992	+	8.55683i	0.244878	+	0.480600i	−0.735552	+	0.677468i	$0.763077\pi$
$318$		0			0
$319$			4.99187i			0.279491i
$320$		0			0
$321$	6.15051	−	38.8328i	0.343288	−	2.16743i
$322$		0			0
$323$	7.92873	−	2.57620i	0.441166	−	0.143344i
$324$		0			0
$325$	3.70878	−	3.70878i	0.205726	−	0.205726i
$326$		0			0
$327$	42.4881			2.34960
$328$		0			0
$329$	29.8603			1.64625
$330$		0			0
$331$	−3.24814	+	3.24814i	−0.178534	+	0.178534i	−0.790716	−	0.612183i	$-0.790292\pi$
$331$	−3.24814	+	3.24814i	−0.178534	+	0.178534i	0.612183	+	0.790716i	$0.290292\pi$
$332$		0			0
$333$	−5.57133	+	1.81024i	−0.305307	+	0.0992003i
$334$		0			0
$335$	0.241216	−	1.52298i	0.0131790	−	0.0832092i
$336$		0			0
$337$			17.7306i			0.965849i	0.875662	+	0.482924i	$0.160425\pi$
$337$			17.7306i			0.965849i	−0.875662	+	0.482924i	$0.839575\pi$
$338$		0			0
$339$	−10.3263	−	20.2666i	−0.560849	−	1.10073i
$340$		0			0
$341$	10.4377	−	1.65317i	0.565232	−	0.0895240i
$342$		0			0
$343$	8.22572	−	16.1439i	0.444147	−	0.871688i
$344$		0			0
$345$	−2.21971	+	1.13100i	−0.119505	+	0.0608908i
$346$		0			0
$347$	−15.9671	−	2.52894i	−0.857160	−	0.135761i	−0.287640	−	0.957739i	$-0.592871\pi$
$347$	−15.9671	−	2.52894i	−0.857160	−	0.135761i	−0.569520	+	0.821978i	$0.692871\pi$
$348$		0			0
$349$	−6.28967	−	8.65699i	−0.336678	−	0.463398i	0.606789	−	0.794863i	$-0.292457\pi$
$349$	−6.28967	−	8.65699i	−0.336678	−	0.463398i	−0.943468	+	0.331465i	$0.892457\pi$
$350$		0			0
$351$	5.33437	+	3.87565i	0.284727	+	0.206867i
$352$		0			0
$353$	21.0319	−	15.2806i	1.11942	−	0.813304i	0.135297	−	0.990805i	$-0.456801\pi$
$353$	21.0319	−	15.2806i	1.11942	−	0.813304i	0.984121	+	0.177501i	$0.0568012\pi$
$354$		0			0
$355$	0.774841	+	0.774841i	0.0411243	+	0.0411243i
$356$		0			0
$357$	−25.1752	−	12.8274i	−1.33241	−	0.678899i
$358$		0			0
$359$	3.00578	−	9.25084i	0.158639	−	0.488241i	−0.839872	−	0.542784i	$-0.817370\pi$
$359$	3.00578	−	9.25084i	0.158639	−	0.488241i	0.998511	+	0.0545433i	$0.0173703\pi$
$360$		0			0
$361$	−13.1272	−	4.26529i	−0.690906	−	0.224489i
$362$		0			0
$363$	0.204279	+	1.28977i	0.0107219	+	0.0676952i
$364$		0			0
$365$	0.391454	+	1.20477i	0.0204896	+	0.0630606i
$366$		0			0
$367$	−13.2160	+	18.1902i	−0.689868	+	0.949522i	−0.999999	−	0.00117139i	$-0.999627\pi$
$367$	−13.2160	+	18.1902i	−0.689868	+	0.949522i	0.310131	+	0.950694i	$0.399627\pi$
$368$		0			0
$369$	32.5172	+	6.86890i	1.69278	+	0.357581i
$370$		0			0
$371$	0.860205	−	1.18397i	0.0446596	−	0.0614687i
$372$		0			0
$373$	−0.994171	−	3.05974i	−0.0514762	−	0.158428i	0.922014	−	0.387157i	$-0.126543\pi$
$373$	−0.994171	−	3.05974i	−0.0514762	−	0.158428i	−0.973490	+	0.228730i	$0.926543\pi$
$374$		0			0
$375$	0.519086	+	3.27738i	0.0268055	+	0.169243i
$376$		0			0
$377$	−1.47536	−	0.479372i	−0.0759847	−	0.0246889i
$378$		0			0
$379$	5.92193	−	18.2258i	0.304189	−	0.936198i	−0.675789	−	0.737095i	$-0.736197\pi$
$379$	5.92193	−	18.2258i	0.304189	−	0.936198i	0.979978	−	0.199103i	$-0.0638029\pi$
$380$		0			0
$381$	20.6671	+	10.5304i	1.05881	+	0.539490i
$382$		0			0
$383$	−20.6909	−	20.6909i	−1.05726	−	1.05726i	−0.998258	−	0.0589972i	$-0.981210\pi$
$383$	−20.6909	−	20.6909i	−1.05726	−	1.05726i	−0.0589972	−	0.998258i	$-0.518790\pi$
$384$		0			0
$385$	0.858318	−	0.623605i	0.0437439	−	0.0317818i
$386$		0			0
$387$	4.16974	+	3.02949i	0.211960	+	0.153998i
$388$		0			0
$389$	−5.16511	−	7.10917i	−0.261882	−	0.360449i	0.657746	−	0.753239i	$-0.271510\pi$
$389$	−5.16511	−	7.10917i	−0.261882	−	0.360449i	−0.919628	+	0.392790i	$0.871510\pi$
$390$		0			0
$391$	−27.0803	−	4.28910i	−1.36951	−	0.216909i
$392$		0			0
$393$	29.0331	−	14.7931i	1.46453	−	0.746214i
$394$		0			0
$395$	−0.565673	+	1.11020i	−0.0284621	+	0.0558600i
$396$		0			0
$397$	−24.8449	+	3.93505i	−1.24693	+	0.197495i	−0.744795	−	0.667294i	$-0.767453\pi$
$397$	−24.8449	+	3.93505i	−1.24693	+	0.197495i	−0.502137	+	0.864788i	$0.667453\pi$
$398$		0			0
$399$	−7.99676	−	15.6945i	−0.400339	−	0.785709i
$400$		0			0
$401$			28.1172i			1.40411i	0.712124	+	0.702054i	$0.247733\pi$
$401$			28.1172i			1.40411i	−0.712124	+	0.702054i	$0.752267\pi$
$402$		0			0
$403$	−0.513740	+	3.24363i	−0.0255912	+	0.161577i
$404$		0			0
$405$	−0.261591	+	0.0849960i	−0.0129986	+	0.00422349i
$406$		0			0
$407$	2.70121	−	2.70121i	0.133894	−	0.133894i
$408$		0			0
$409$	1.43475			0.0709440			0.0354720	−	0.999371i	$-0.488707\pi$
$409$	1.43475			0.0709440			0.0354720	+	0.999371i	$0.488707\pi$
$410$		0			0
$411$	17.2726			0.851992
$412$		0			0
$413$	3.71053	−	3.71053i	0.182583	−	0.182583i
$414$		0			0
$415$	0.0701399	−	0.0227898i	0.00344303	−	0.00111871i
$416$		0			0
$417$	−7.90224	+	49.8928i	−0.386974	+	2.44326i
$418$		0			0
$419$			15.5755i			0.760912i	0.924799	+	0.380456i	$0.124233\pi$
$419$			15.5755i			0.760912i	−0.924799	+	0.380456i	$0.875767\pi$
$420$		0			0
$421$	−3.37083	−	6.61562i	−0.164284	−	0.322426i	0.794159	−	0.607710i	$-0.207912\pi$
$421$	−3.37083	−	6.61562i	−0.164284	−	0.322426i	−0.958443	+	0.285285i	$0.907912\pi$
$422$		0			0
$423$	56.7003	−	8.98045i	2.75687	−	0.436645i
$424$		0			0
$425$	−8.27857	+	16.2476i	−0.401570	+	0.788125i
$426$		0			0
$427$	−24.3889	+	12.4268i	−1.18026	+	0.601373i
$428$		0			0
$429$	−10.0634	−	1.59388i	−0.485864	−	0.0769533i
$430$		0			0
$431$	−20.1133	−	27.6836i	−0.968824	−	1.33347i	−0.942639	−	0.333815i	$-0.891664\pi$
$431$	−20.1133	−	27.6836i	−0.968824	−	1.33347i	−0.0261853	−	0.999657i	$-0.508336\pi$
$432$		0			0
$433$	−6.78471	−	4.92938i	−0.326053	−	0.236891i	0.412701	−	0.910866i	$-0.364585\pi$
$433$	−6.78471	−	4.92938i	−0.326053	−	0.236891i	−0.738754	+	0.673975i	$0.764585\pi$
$434$		0			0
$435$	0.396453	−	0.288040i	0.0190085	−	0.0138105i
$436$		0			0
$437$	−12.0863	−	12.0863i	−0.578166	−	0.578166i
$438$		0			0
$439$	−21.8040	−	11.1097i	−1.04065	−	0.530236i	−0.151786	−	0.988413i	$-0.548502\pi$
$439$	−21.8040	−	11.1097i	−1.04065	−	0.530236i	−0.888861	+	0.458178i	$0.848502\pi$
$440$		0			0
$441$	−0.463260	+	1.42577i	−0.0220600	+	0.0678936i
$442$		0			0
$443$	13.1456	+	4.27126i	0.624565	+	0.202933i	0.604166	−	0.796858i	$-0.293506\pi$
$443$	13.1456	+	4.27126i	0.624565	+	0.202933i	0.0203990	+	0.999792i	$0.493506\pi$
$444$		0			0
$445$	−0.0874436	−	0.552097i	−0.00414522	−	0.0261719i
$446$		0			0
$447$	−0.957532	−	2.94698i	−0.0452897	−	0.139387i
$448$		0			0
$449$	0.627367	−	0.863496i	0.0296073	−	0.0407509i	−0.793957	−	0.607974i	$-0.791982\pi$
$449$	0.627367	−	0.863496i	0.0296073	−	0.0407509i	0.823564	+	0.567223i	$0.191982\pi$
$450$		0			0
$451$	−20.9272	+	5.63571i	−0.985422	+	0.265375i
$452$		0			0
$453$	−22.1061	+	30.4265i	−1.03864	+	1.42956i
$454$		0			0
$455$	0.101883	+	0.313562i	0.00477633	+	0.0147000i
$456$		0			0
$457$	−4.71510	−	29.7700i	−0.220563	−	1.39258i	−0.810787	−	0.585342i	$-0.800960\pi$
$457$	−4.71510	−	29.7700i	−0.220563	−	1.39258i	0.590223	−	0.807240i	$-0.299040\pi$
$458$		0			0
$459$	−21.8019	−	7.08386i	−1.01762	−	0.330646i
$460$		0			0
$461$	0.963390	−	2.96501i	0.0448695	−	0.138094i	−0.926112	−	0.377249i	$-0.876870\pi$
$461$	0.963390	−	2.96501i	0.0448695	−	0.138094i	0.970982	+	0.239154i	$0.0768702\pi$
$462$		0			0
$463$	6.30485	+	3.21248i	0.293011	+	0.149297i	0.594317	−	0.804231i	$-0.297423\pi$
$463$	6.30485	+	3.21248i	0.293011	+	0.149297i	−0.301306	+	0.953528i	$0.597423\pi$
$464$		0			0
$465$	−0.733567	−	0.733567i	−0.0340183	−	0.0340183i
$466$		0			0
$467$	−31.9737	+	23.2303i	−1.47957	+	1.07497i	−0.501873	+	0.864941i	$0.667356\pi$
$467$	−31.9737	+	23.2303i	−1.47957	+	1.07497i	−0.977695	+	0.210028i	$0.932644\pi$
$468$		0			0
$469$	−29.0082	−	21.0757i	−1.33947	−	0.973184i
$470$		0			0
$471$	27.5751	+	37.9539i	1.27060	+	1.74882i
$472$		0			0
$473$	−3.31965	−	0.525780i	−0.152638	−	0.0241754i
$474$		0			0
$475$	−10.1289	+	5.16096i	−0.464748	+	0.236801i
$476$		0			0
$477$	1.27733	−	2.50690i	0.0584848	−	0.114783i
$478$		0			0
$479$	−11.5501	+	1.82935i	−0.527737	+	0.0835853i	−0.414617	−	0.909996i	$-0.636084\pi$
$479$	−11.5501	+	1.82935i	−0.527737	+	0.0835853i	−0.113120	+	0.993581i	$0.536084\pi$
$480$		0			0
$481$	0.538949	+	1.05775i	0.0245740	+	0.0482291i
$482$		0			0
$483$			57.9300i			2.63591i
$484$		0			0
$485$	−0.0501725	+	0.316776i	−0.00227821	+	0.0143841i
$486$		0			0
$487$	23.9864	−	7.79365i	1.08693	−	0.353164i	0.289869	−	0.957066i	$-0.406388\pi$
$487$	23.9864	−	7.79365i	1.08693	−	0.353164i	0.797058	+	0.603903i	$0.206388\pi$
$488$		0			0
$489$	−29.6115	+	29.6115i	−1.33908	+	1.33908i
$490$		0			0
$491$	31.5085			1.42196			0.710980	−	0.703212i	$-0.248252\pi$
$491$	31.5085			1.42196			0.710980	+	0.703212i	$0.248252\pi$
$492$		0			0
$493$	5.39328			0.242901
$494$		0			0
$495$	1.44227	−	1.44227i	0.0648254	−	0.0648254i
$496$		0			0
$497$	24.2339	−	7.87407i	1.08704	−	0.353200i
$498$		0			0
$499$	−0.773481	+	4.88356i	−0.0346257	+	0.218618i	−0.998934	−	0.0461643i	$-0.985300\pi$
$499$	−0.773481	+	4.88356i	−0.0346257	+	0.218618i	0.964308	+	0.264783i	$0.0853002\pi$
$500$		0			0
$501$		−	33.2509i		−	1.48554i
$502$		0			0
$503$	11.0443	+	21.6756i	0.492439	+	0.966466i	0.994804	+	0.101810i	$0.0324635\pi$
$503$	11.0443	+	21.6756i	0.492439	+	0.966466i	−0.502365	+	0.864656i	$0.667537\pi$
$504$		0			0
$505$	1.08485	−	0.171823i	0.0482751	−	0.00764602i
$506$		0			0
$507$	−15.4530	+	30.3283i	−0.686294	+	1.34693i
$508$		0			0
$509$	29.2644	−	14.9110i	1.29712	−	0.660917i	0.337266	−	0.941409i	$-0.390498\pi$
$509$	29.2644	−	14.9110i	1.29712	−	0.660917i	0.959856	+	0.280493i	$0.0904978\pi$
$510$		0			0
$511$	29.0942	+	4.60807i	1.28705	+	0.203849i
$512$		0			0
$513$	−8.40003	−	11.5617i	−0.370870	−	0.510459i
$514$		0			0
$515$	−0.590165	−	0.428780i	−0.0260058	−	0.0188943i
$516$		0			0
$517$	−30.2862	+	22.0042i	−1.33198	+	0.967743i
$518$		0			0
$519$	−4.08519	−	4.08519i	−0.179320	−	0.179320i
$520$		0			0
$521$	−37.3756	−	19.0438i	−1.63745	−	0.834325i	−0.997844	−	0.0656258i	$-0.979096\pi$
$521$	−37.3756	−	19.0438i	−1.63745	−	0.834325i	−0.639611	−	0.768699i	$-0.720904\pi$
$522$		0			0
$523$	4.76782	−	14.6739i	0.208482	−	0.641643i	−0.791070	−	0.611726i	$-0.790476\pi$
$523$	4.76782	−	14.6739i	0.208482	−	0.641643i	0.999552	−	0.0299172i	$-0.00952435\pi$
$524$		0			0
$525$	36.6425	+	11.9059i	1.59921	+	0.519615i
$526$		0			0
$527$	−1.78610	−	11.2770i	−0.0778037	−	0.491233i
$528$		0			0
$529$	10.2637	+	31.5884i	0.446247	+	1.37341i
$530$		0			0
$531$	5.92982	−	8.16169i	0.257332	−	0.354187i
$532$		0			0
$533$	0.344004	−	6.72626i	0.0149005	−	0.291347i
$534$		0			0
$535$	0.937529	−	1.29040i	0.0405329	−	0.0557888i
$536$		0			0
$537$	15.7969	+	48.6180i	0.681688	+	2.09802i
$538$		0			0
$539$	−0.152931	−	0.965568i	−0.00658720	−	0.0415900i
$540$		0			0
$541$	8.26506	+	2.68548i	0.355343	+	0.115458i	0.481248	−	0.876584i	$-0.340184\pi$
$541$	8.26506	+	2.68548i	0.355343	+	0.115458i	−0.125905	+	0.992042i	$0.540184\pi$
$542$		0			0
$543$	−1.56550	+	4.81810i	−0.0671819	+	0.206765i
$544$		0			0
$545$	1.53580	+	0.782530i	0.0657865	+	0.0335199i
$546$		0			0
$547$	−1.94269	−	1.94269i	−0.0830635	−	0.0830635i	0.664354	−	0.747418i	$-0.268707\pi$
$547$	−1.94269	−	1.94269i	−0.0830635	−	0.0830635i	−0.747418	+	0.664354i	$0.768707\pi$
$548$		0			0
$549$	−42.5736	+	30.9315i	−1.81700	+	1.32013i
$550$		0			0
$551$	2.72010	+	1.97627i	0.115880	+	0.0841919i
$552$		0			0
$553$	17.0305	+	23.4404i	0.724209	+	0.996788i
$554$		0			0
$555$	−0.370394	−	0.0586647i	−0.0157224	−	0.00249018i
$556$		0			0
$557$	−29.7769	+	15.1721i	−1.26169	+	0.642862i	−0.951452	−	0.307797i	$-0.900408\pi$
$557$	−29.7769	+	15.1721i	−1.26169	+	0.642862i	−0.310236	+	0.950660i	$0.600408\pi$
$558$		0			0
$559$	0.474183	−	0.930636i	0.0200558	−	0.0393617i
$560$		0			0
$561$	34.9869	−	5.54138i	1.47715	−	0.233957i
$562$		0			0
$563$	−7.71260	−	15.1368i	−0.325047	−	0.637941i	0.669432	−	0.742873i	$-0.266537\pi$
$563$	−7.71260	−	15.1368i	−0.325047	−	0.637941i	−0.994479	+	0.104932i	$0.966537\pi$
$564$		0			0
$565$		−	0.922756i		−	0.0388206i
$566$		0			0
$567$	−1.00055	+	6.31721i	−0.0420191	+	0.265298i
$568$		0			0
$569$	24.8527	−	8.07512i	1.04188	−	0.338526i	0.262402	−	0.964959i	$-0.415486\pi$
$569$	24.8527	−	8.07512i	1.04188	−	0.338526i	0.779476	+	0.626432i	$0.215486\pi$
$570$		0			0
$571$	1.00428	−	1.00428i	0.0420278	−	0.0420278i	−0.685781	−	0.727808i	$-0.740539\pi$
$571$	1.00428	−	1.00428i	0.0420278	−	0.0420278i	0.727808	+	0.685781i	$0.240539\pi$
$572$		0			0
$573$	15.6243			0.652714
$574$		0			0
$575$	37.3869			1.55914
$576$		0			0
$577$	23.1743	−	23.1743i	0.964760	−	0.964760i	−0.0346401	−	0.999400i	$-0.511028\pi$
$577$	23.1743	−	23.1743i	0.964760	−	0.964760i	0.999400	+	0.0346401i	$0.0110285\pi$
$578$		0			0
$579$	−17.8513	+	5.80022i	−0.741873	+	0.241049i
$580$		0			0
$581$	0.268275	−	1.69382i	0.0111299	−	0.0702715i
$582$		0			0
$583$			1.83475i			0.0759875i
$584$		0			0
$585$	0.287764	+	0.564769i	0.0118976	+	0.0233503i
$586$		0			0
$587$	7.53663	−	1.19368i	0.311070	−	0.0492686i	0.00105233	−	0.999999i	$-0.499665\pi$
$587$	7.53663	−	1.19368i	0.311070	−	0.0492686i	0.310018	+	0.950731i	$0.399665\pi$
$588$		0			0
$589$	3.23143	−	6.34204i	0.133149	−	0.261319i
$590$		0			0
$591$	−10.8896	+	5.54855i	−0.447940	+	0.228237i
$592$		0			0
$593$	−41.5892	−	6.58708i	−1.70786	−	0.270499i	−0.775322	−	0.631566i	$-0.782413\pi$
$593$	−41.5892	−	6.58708i	−1.70786	−	0.270499i	−0.932540	+	0.361067i	$0.882413\pi$
$594$		0			0
$595$	−0.673750	−	0.927337i	−0.0276210	−	0.0380171i
$596$		0			0
$597$	37.0324	+	26.9056i	1.51563	+	1.10117i
$598$		0			0
$599$	−37.0626	+	26.9276i	−1.51434	+	1.10023i	−0.550129	+	0.835079i	$0.685422\pi$
$599$	−37.0626	+	26.9276i	−1.51434	+	1.10023i	−0.964207	+	0.265151i	$0.914578\pi$
$600$		0			0
$601$	−8.39569	−	8.39569i	−0.342467	−	0.342467i	0.514827	−	0.857294i	$-0.327856\pi$
$601$	−8.39569	−	8.39569i	−0.342467	−	0.342467i	−0.857294	+	0.514827i	$0.827856\pi$
$602$		0			0
$603$	−61.4208	−	31.2955i	−2.50125	−	1.27445i
$604$		0			0
$605$	−0.0163705	+	0.0503831i	−0.000665554	+	0.00204837i
$606$		0			0
$607$	22.8222	+	7.41539i	0.926325	+	0.300981i	0.733059	−	0.680165i	$-0.238092\pi$
$607$	22.8222	+	7.41539i	0.926325	+	0.300981i	0.193266	+	0.981146i	$0.438092\pi$
$608$		0			0
$609$	−1.78261	−	11.2549i	−0.0722348	−	0.456073i
$610$		0			0
$611$	−3.59498	−	11.0642i	−0.145437	−	0.447610i
$612$		0			0
$613$	−10.8769	+	14.9708i	−0.439315	+	0.604665i	−0.970060	−	0.242867i	$-0.921912\pi$
$613$	−10.8769	+	14.9708i	−0.439315	+	0.604665i	0.530745	+	0.847532i	$0.321912\pi$
$614$		0			0
$615$	1.65512	+	1.33684i	0.0667409	+	0.0539065i
$616$		0			0
$617$	−0.798604	+	1.09918i	−0.0321506	+	0.0442515i	−0.824790	−	0.565440i	$-0.808707\pi$
$617$	−0.798604	+	1.09918i	−0.0321506	+	0.0442515i	0.792639	+	0.609691i	$0.208707\pi$
$618$		0			0
$619$	−12.9896	−	39.9780i	−0.522097	−	1.60685i	−0.769985	−	0.638062i	$-0.779736\pi$
$619$	−12.9896	−	39.9780i	−0.522097	−	1.60685i	0.247888	−	0.968789i	$-0.420264\pi$
$620$		0			0
$621$	7.35243	+	46.4214i	0.295043	+	1.86283i
$622$		0			0
$623$	−12.3621	−	4.01668i	−0.495276	−	0.160925i
$624$		0			0
$625$	7.66300	−	23.5843i	0.306520	−	0.943371i
$626$		0			0
$627$	19.6762	+	10.0255i	0.785792	+	0.400381i
$628$		0			0
$629$	−2.91842	−	2.91842i	−0.116365	−	0.116365i
$630$		0			0
$631$	−29.2153	+	21.2262i	−1.16304	+	0.845001i	−0.990160	−	0.139941i	$-0.955309\pi$
$631$	−29.2153	+	21.2262i	−1.16304	+	0.845001i	−0.172884	+	0.984942i	$0.555309\pi$
$632$		0			0
$633$	−57.8390	−	42.0225i	−2.29889	−	1.67024i
$634$		0			0
$635$	0.553102	+	0.761280i	0.0219492	+	0.0302105i
$636$		0			0
$637$	0.300061	+	0.0475251i	0.0118889	+	0.00188301i
$638$		0			0
$639$	43.6485	−	22.2400i	1.72671	−	0.879802i
$640$		0			0
$641$	−20.0951	+	39.4388i	−0.793708	+	1.55774i	0.0358741	+	0.999356i	$0.488578\pi$
$641$	−20.0951	+	39.4388i	−0.793708	+	1.55774i	−0.829583	+	0.558384i	$0.811422\pi$
$642$		0			0
$643$	12.3017	−	1.94839i	0.485131	−	0.0768372i	0.0909219	−	0.995858i	$-0.471019\pi$
$643$	12.3017	−	1.94839i	0.485131	−	0.0768372i	0.394209	+	0.919021i	$0.371019\pi$
$644$		0			0
$645$	0.149792	+	0.293984i	0.00589806	+	0.0115756i
$646$		0			0
$647$			15.7465i			0.619061i	0.950890	+	0.309530i	$0.100172\pi$
$647$			15.7465i			0.619061i	−0.950890	+	0.309530i	$0.899828\pi$
$648$		0			0
$649$	−1.02914	+	6.49776i	−0.0403974	+	0.255059i
$650$		0			0
$651$	−22.9430	+	7.45463i	−0.899206	+	0.292170i
$652$		0			0
$653$	13.7349	−	13.7349i	0.537489	−	0.537489i	−0.385301	−	0.922791i	$-0.625903\pi$
$653$	13.7349	−	13.7349i	0.537489	−	0.537489i	0.922791	+	0.385301i	$0.125903\pi$
$654$		0			0
$655$	1.32190			0.0516511
$656$		0			0
$657$	56.6316			2.20941
$658$		0			0
$659$	8.94994	−	8.94994i	0.348640	−	0.348640i	−0.510963	−	0.859603i	$-0.670711\pi$
$659$	8.94994	−	8.94994i	0.348640	−	0.348640i	0.859603	+	0.510963i	$0.170711\pi$
$660$		0			0
$661$	35.5255	−	11.5429i	1.38178	−	0.448968i	0.478527	−	0.878073i	$-0.341171\pi$
$661$	35.5255	−	11.5429i	1.38178	−	0.448968i	0.903255	+	0.429105i	$0.141171\pi$
$662$		0			0
$663$	−1.72205	+	10.8726i	−0.0668788	+	0.422256i
$664$		0			0
$665$		−	0.714586i		−	0.0277105i
$666$		0			0
$667$	−5.02008	−	9.85246i	−0.194378	−	0.381489i
$668$		0			0
$669$	9.38166	−	1.48591i	0.362716	−	0.0574486i
$670$		0			0
$671$	15.5794	−	30.5763i	0.601436	−	1.18038i
$672$		0			0
$673$	−9.32618	+	4.75192i	−0.359498	+	0.183173i	−0.624405	−	0.781101i	$-0.714659\pi$
$673$	−9.32618	+	4.75192i	−0.359498	+	0.183173i	0.264908	+	0.964274i	$0.414659\pi$
$674$		0			0
$675$	30.8741	+	4.88997i	1.18834	+	0.188215i
$676$		0			0
$677$	9.95839	+	13.7066i	0.382732	+	0.526786i	0.956306	−	0.292368i	$-0.0944434\pi$
$677$	9.95839	+	13.7066i	0.382732	+	0.526786i	−0.573574	+	0.819154i	$0.694443\pi$
$678$		0			0
$679$	6.03364	+	4.38370i	0.231550	+	0.168231i
$680$		0			0
$681$	17.8455	−	12.9655i	0.683841	−	0.496840i
$682$		0			0
$683$	14.4614	+	14.4614i	0.553350	+	0.553350i	0.927406	−	0.374056i	$-0.122033\pi$
$683$	14.4614	+	14.4614i	0.553350	+	0.553350i	−0.374056	+	0.927406i	$0.622033\pi$
$684$		0			0
$685$	0.624345	+	0.318120i	0.0238550	+	0.0121547i
$686$		0			0
$687$	4.39851	−	13.5372i	0.167813	−	0.516477i
$688$		0			0
$689$	−0.542263	−	0.176192i	−0.0206586	−	0.00671238i
$690$		0			0
$691$	1.41031	+	8.90432i	0.0536506	+	0.338736i	0.999884	+	0.0152509i	$0.00485471\pi$
$691$	1.41031	+	8.90432i	0.0536506	+	0.338736i	−0.946233	+	0.323486i	$0.895145\pi$
$692$		0			0
$693$	−14.6566	−	45.1085i	−0.556759	−	1.71353i
$694$		0			0
$695$	−1.20455	+	1.65792i	−0.0456911	+	0.0628884i
$696$		0			0
$697$	6.08889	+	22.6100i	0.230633	+	0.856413i
$698$		0			0
$699$	−18.0078	+	24.7857i	−0.681119	+	0.937480i
$700$		0			0
$701$	3.66441	+	11.2779i	0.138403	+	0.425960i	0.996104	−	0.0881889i	$-0.0281079\pi$
$701$	3.66441	+	11.2779i	0.138403	+	0.425960i	−0.857701	+	0.514149i	$0.828108\pi$
$702$		0			0
$703$	−0.402504	−	2.54131i	−0.0151807	−	0.0958474i
$704$		0			0
$705$	3.49513	+	1.13564i	0.131634	+	0.0427706i
$706$		0			0
$707$	7.89260	−	24.2909i	0.296832	−	0.913555i
$708$		0			0
$709$	36.6676	+	18.6831i	1.37708	+	0.701658i	0.976684	−	0.214683i	$-0.0688718\pi$
$709$	36.6676	+	18.6831i	1.37708	+	0.701658i	0.400398	+	0.916341i	$0.368872\pi$
$710$		0			0
$711$	39.3881	+	39.3881i	1.47717	+	1.47717i
$712$		0			0
$713$	−18.9383	+	13.7595i	−0.709246	+	0.515298i
$714$		0			0
$715$	−0.334402	−	0.242957i	−0.0125059	−	0.00908608i
$716$		0			0
$717$	−15.5498	−	21.4024i	−0.580716	−	0.799287i
$718$		0			0
$719$	24.4544	+	3.87320i	0.911996	+	0.144446i	0.594762	−	0.803902i	$-0.297246\pi$
$719$	24.4544	+	3.87320i	0.911996	+	0.144446i	0.317233	+	0.948348i	$0.397246\pi$
$720$		0			0
$721$	−15.1142	+	7.70108i	−0.562883	+	0.286803i
$722$		0			0
$723$	−36.8227	+	72.2685i	−1.36945	+	2.68770i
$724$		0			0
$725$	−7.26372	+	1.15046i	−0.269768	+	0.0427270i
$726$		0			0
$727$	0.177225	+	0.347823i	0.00657290	+	0.0129000i	0.894270	−	0.447529i	$-0.147696\pi$
$727$	0.177225	+	0.347823i	0.00657290	+	0.0129000i	−0.887697	+	0.460429i	$0.847696\pi$
$728$		0			0
$729$		−	41.5244i		−	1.53794i
$730$		0			0
$731$	−0.568059	+	3.58659i	−0.0210104	+	0.132655i
$732$		0			0
$733$	−9.37877	+	3.04735i	−0.346413	+	0.112556i	−0.477055	−	0.878873i	$-0.658296\pi$
$733$	−9.37877	+	3.04735i	−0.346413	+	0.112556i	0.130643	+	0.991430i	$0.458296\pi$
$734$		0			0
$735$	−0.0678607	+	0.0678607i	−0.00250308	+	0.00250308i
$736$		0			0
$737$	44.9527			1.65585
$738$		0			0
$739$	−13.8121			−0.508087			−0.254044	−	0.967193i	$-0.581761\pi$
$739$	−13.8121			−0.508087			−0.254044	+	0.967193i	$0.581761\pi$
$740$		0			0
$741$	−4.85258	+	4.85258i	−0.178264	+	0.178264i
$742$		0			0
$743$	24.8949	−	8.08883i	0.913304	−	0.296750i	0.185587	−	0.982628i	$-0.440581\pi$
$743$	24.8949	−	8.08883i	0.913304	−	0.296750i	0.727717	+	0.685878i	$0.240581\pi$
$744$		0			0
$745$	0.0196648	−	0.124159i	0.000720464	−	0.00454883i
$746$		0			0
$747$		−	3.29701i		−	0.120631i
$748$		0			0
$749$	−16.8384	−	33.0473i	−0.615263	−	1.20752i
$750$		0			0
$751$	20.6029	−	3.26318i	0.751812	−	0.119075i	0.231244	−	0.972896i	$-0.425720\pi$
$751$	20.6029	−	3.26318i	0.751812	−	0.119075i	0.520568	+	0.853820i	$0.325720\pi$
$752$		0			0
$753$	−8.58455	+	16.8481i	−0.312839	+	0.613980i
$754$		0			0
$755$	−1.35945	+	0.692672i	−0.0494753	+	0.0252089i
$756$		0			0
$757$	44.0377	+	6.97489i	1.60058	+	0.253507i	0.891970	−	0.452095i	$-0.149323\pi$
$757$	44.0377	+	6.97489i	1.60058	+	0.253507i	0.708609	+	0.705602i	$0.249323\pi$
$758$		0			0
$759$	−42.6889	−	58.7563i	−1.54951	−	2.13272i
$760$		0			0
$761$	−35.6363	−	25.8913i	−1.29182	−	0.938559i	−0.291976	−	0.956426i	$-0.594313\pi$
$761$	−35.6363	−	25.8913i	−1.29182	−	0.938559i	−0.999840	+	0.0178662i	$0.994313\pi$
$762$		0			0
$763$	32.4266	−	23.5593i	1.17392	−	0.852903i
$764$		0			0
$765$	−1.55825	−	1.55825i	−0.0563386	−	0.0563386i
$766$		0			0
$767$	−1.82159	−	0.928148i	−0.0657739	−	0.0335135i
$768$		0			0
$769$	−5.91420	+	18.2020i	−0.213272	+	0.656383i	0.786000	+	0.618226i	$0.212148\pi$
$769$	−5.91420	+	18.2020i	−0.213272	+	0.656383i	−0.999272	+	0.0381563i	$0.987852\pi$
$770$		0			0
$771$	−11.9662	−	3.88806i	−0.430952	−	0.140025i
$772$		0			0
$773$	4.60071	+	29.0477i	0.165476	+	1.04477i	0.920974	+	0.389624i	$0.127395\pi$
$773$	4.60071	+	29.0477i	0.165476	+	1.04477i	−0.755498	+	0.655151i	$0.772605\pi$
$774$		0			0
$775$	4.81107	+	14.8070i	0.172819	+	0.531882i
$776$		0			0
$777$	−5.12569	+	7.05490i	−0.183883	+	0.253093i
$778$		0			0
$779$	−5.21408	+	13.6345i	−0.186814	+	0.488507i
$780$		0			0
$781$	−18.7771	+	25.8445i	−0.671897	+	0.924787i
$782$		0			0
$783$	−2.85693	−	8.79274i	−0.102098	−	0.314227i
$784$		0			0
$785$	0.297727	+	1.87978i	0.0106263	+	0.0670921i
$786$		0			0
$787$	22.7158	+	7.38080i	0.809730	+	0.263097i	0.684483	−	0.729028i	$-0.260028\pi$
$787$	22.7158	+	7.38080i	0.809730	+	0.263097i	0.125246	+	0.992126i	$0.460028\pi$
$788$		0			0
$789$	11.0730	−	34.0793i	0.394211	−	1.21326i
$790$		0			0
$791$	−19.1186	−	9.74142i	−0.679780	−	0.346365i
$792$		0			0
$793$	7.54078	+	7.54078i	0.267781	+	0.267781i
$794$		0			0
$795$	0.145715	−	0.105868i	0.00516798	−	0.00375476i
$796$		0			0
$797$	26.5246	+	19.2712i	0.939548	+	0.682622i	0.948312	−	0.317340i	$-0.102790\pi$
$797$	26.5246	+	19.2712i	0.939548	+	0.682622i	−0.00876372	+	0.999962i	$0.502790\pi$
$798$		0			0
$799$	23.7736	+	32.7215i	0.841049	+	1.15760i
$800$		0			0
$801$	−24.6818	−	3.90921i	−0.872088	−	0.138125i
$802$		0			0
$803$	−32.9049	+	16.7659i	−1.16119	+	0.591656i
$804$		0			0
$805$	−1.06693	+	2.09398i	−0.0376045	+	0.0738030i
$806$		0			0
$807$	−10.0041	+	1.58449i	−0.352161	+	0.0557768i
$808$		0			0
$809$	−9.00467	−	17.6727i	−0.316587	−	0.621338i	0.676798	−	0.736169i	$-0.263367\pi$
$809$	−9.00467	−	17.6727i	−0.316587	−	0.621338i	−0.993385	+	0.114831i	$0.963367\pi$
$810$		0			0
$811$		−	12.6254i		−	0.443338i	−0.975122	−	0.221669i	$-0.928850\pi$
$811$		−	12.6254i		−	0.443338i	0.975122	−	0.221669i	$-0.0711505\pi$
$812$		0			0
$813$	−1.71346	+	10.8184i	−0.0600936	+	0.379416i
$814$		0			0
$815$	−1.61573	+	0.524983i	−0.0565966	+	0.0183894i
$816$		0			0
$817$	−1.60074	+	1.60074i	−0.0560028	+	0.0560028i
$818$		0			0
$819$	14.7394			0.515035
$820$		0			0
$821$	−3.71560			−0.129675			−0.0648376	−	0.997896i	$-0.520653\pi$
$821$	−3.71560			−0.129675			−0.0648376	+	0.997896i	$0.520653\pi$
$822$		0			0
$823$	−30.0144	+	30.0144i	−1.04624	+	1.04624i	−0.0473578	+	0.998878i	$0.515080\pi$
$823$	−30.0144	+	30.0144i	−1.04624	+	1.04624i	−0.998878	+	0.0473578i	$0.984920\pi$
$824$		0			0
$825$	−45.9387	+	14.9264i	−1.59938	+	0.519670i
$826$		0			0
$827$	−2.13027	+	13.4500i	−0.0740766	+	0.467702i	0.922567	+	0.385837i	$0.126087\pi$
$827$	−2.13027	+	13.4500i	−0.0740766	+	0.467702i	−0.996643	+	0.0818642i	$0.973913\pi$
$828$		0			0
$829$			38.0361i			1.32105i	0.750805	+	0.660524i	$0.229666\pi$
$829$			38.0361i			1.32105i	−0.750805	+	0.660524i	$0.770334\pi$
$830$		0			0
$831$	−38.9866	−	76.5155i	−1.35243	−	2.65429i
$832$		0			0
$833$	−1.04321	+	0.165228i	−0.0361451	+	0.00572483i
$834$		0			0
$835$	0.612404	−	1.20191i	0.0211931	−	0.0415938i
$836$		0			0
$837$	−17.4389	+	8.88557i	−0.602777	+	0.307130i
$838$		0			0
$839$	7.44308	+	1.17887i	0.256964	+	0.0406991i	0.283587	−	0.958946i	$-0.408475\pi$
$839$	7.44308	+	1.17887i	0.256964	+	0.0406991i	−0.0266234	+	0.999646i	$0.508475\pi$
$840$		0			0
$841$	−15.7673	−	21.7018i	−0.543699	−	0.748337i
$842$		0			0
$843$	12.7352	+	9.25263i	0.438622	+	0.318678i
$844$		0			0
$845$	−1.11715	+	0.811658i	−0.0384312	+	0.0279219i
$846$		0			0
$847$	0.871070	+	0.871070i	0.0299303	+	0.0299303i
$848$		0			0
$849$	−77.3614	−	39.4176i	−2.65504	−	1.35281i
$850$		0			0
$851$	−2.61491	+	8.04786i	−0.0896379	+	0.275877i
$852$		0			0
$853$	−44.7084	−	14.5266i	−1.53079	−	0.497383i	−0.581971	−	0.813210i	$-0.697718\pi$
$853$	−44.7084	−	14.5266i	−1.53079	−	0.497383i	−0.948817	+	0.315827i	$0.897718\pi$
$854$		0			0
$855$	−0.214911	−	1.35690i	−0.00734981	−	0.0464049i
$856$		0			0
$857$	6.41959	+	19.7575i	0.219289	+	0.674903i	0.998821	+	0.0485403i	$0.0154569\pi$
$857$	6.41959	+	19.7575i	0.219289	+	0.674903i	−0.779532	+	0.626362i	$0.784543\pi$
$858$		0			0
$859$	7.73097	−	10.6408i	0.263777	−	0.363058i	−0.656499	−	0.754327i	$-0.727964\pi$
$859$	7.73097	−	10.6408i	0.263777	−	0.363058i	0.920277	+	0.391268i	$0.127964\pi$
$860$		0			0
$861$	45.1710	−	20.1797i	1.53942	−	0.687722i
$862$		0			0
$863$	10.8301	−	14.9063i	0.368661	−	0.507418i	−0.583876	−	0.811843i	$-0.698464\pi$
$863$	10.8301	−	14.9063i	0.368661	−	0.507418i	0.952536	+	0.304425i	$0.0984644\pi$
$864$		0			0
$865$	−0.0724265	−	0.222906i	−0.00246257	−	0.00757902i
$866$		0			0
$867$	1.62389	+	10.2528i	0.0551502	+	0.348204i
$868$		0			0
$869$	−34.5468	−	11.2249i	−1.17192	−	0.380779i
$870$		0			0
$871$	−4.31683	+	13.2858i	−0.146270	+	0.450174i
$872$		0			0
$873$	12.7754	+	6.50940i	0.432382	+	0.220310i
$874$		0			0
$875$	2.21344	+	2.21344i	0.0748280	+	0.0748280i
$876$		0			0
$877$	−15.2047	+	11.0469i	−0.513426	+	0.373026i	−0.814122	−	0.580694i	$-0.802781\pi$
$877$	−15.2047	+	11.0469i	−0.513426	+	0.373026i	0.300696	+	0.953720i	$0.402781\pi$
$878$		0			0
$879$	−46.5273	−	33.8041i	−1.56933	−	1.14018i
$880$		0			0
$881$	6.74048	+	9.27748i	0.227093	+	0.312566i	0.907325	−	0.420431i	$-0.138121\pi$
$881$	6.74048	+	9.27748i	0.227093	+	0.312566i	−0.680232	+	0.732997i	$0.738121\pi$
$882$		0			0
$883$	−36.1792	−	5.73023i	−1.21753	−	0.192837i	−0.485576	−	0.874194i	$-0.661390\pi$
$883$	−36.1792	−	5.73023i	−1.21753	−	0.192837i	−0.731951	+	0.681357i	$0.761390\pi$
$884$		0			0
$885$	0.575433	−	0.293198i	0.0193430	−	0.00985574i
$886$		0			0
$887$	−20.8224	+	40.8663i	−0.699149	+	1.37216i	0.218922	+	0.975742i	$0.429746\pi$
$887$	−20.8224	+	40.8663i	−0.699149	+	1.37216i	−0.918071	+	0.396415i	$0.870254\pi$
$888$		0			0
$889$	21.6120	−	3.42301i	0.724844	−	0.114804i
$890$		0			0
$891$	−3.64037	−	7.14462i	−0.121957	−	0.239354i
$892$		0			0
$893$			25.2145i			0.843772i
$894$		0			0
$895$	−0.324422	+	2.04832i	−0.0108442	+	0.0684678i
$896$		0			0
$897$	21.4650	−	6.97439i	0.716694	−	0.232868i
$898$		0			0
$899$	3.25603	−	3.25603i	0.108595	−	0.108595i
$900$		0			0
$901$	1.98228			0.0660394
$902$		0			0
$903$	7.67240			0.255322
$904$		0			0
$905$	−0.145326	+	0.145326i	−0.00483078	+	0.00483078i
$906$		0			0
$907$	4.33501	−	1.40853i	0.143942	−	0.0467695i	−0.236160	−	0.971714i	$-0.575889\pi$
$907$	4.33501	−	1.40853i	0.143942	−	0.0467695i	0.380102	+	0.924945i	$0.375889\pi$
$908$		0			0
$909$	7.68144	−	48.4987i	0.254777	−	1.60860i
$910$		0			0
$911$		−	0.497074i		−	0.0164688i	−0.999966	−	0.00823439i	$-0.997379\pi$
$911$		−	0.497074i		−	0.0164688i	0.999966	−	0.00823439i	$-0.00262112\pi$
$912$		0			0
$913$	0.976085	+	1.91567i	0.0323037	+	0.0633996i
$914$		0			0
$915$	−3.32732	+	0.526995i	−0.109998	+	0.0174219i
$916$		0			0
$917$	13.9552	−	27.3886i	0.460841	−	0.904452i
$918$		0			0
$919$	19.8412	−	10.1096i	0.654502	−	0.333485i	−0.0950101	−	0.995476i	$-0.530288\pi$
$919$	19.8412	−	10.1096i	0.654502	−	0.333485i	0.749512	+	0.661991i	$0.230288\pi$
$920$		0			0
$921$	−0.638514	−	0.101131i	−0.0210397	−	0.00333237i
$922$		0			0
$923$	−5.83520	−	8.03146i	−0.192068	−	0.264359i
$924$		0			0
$925$	4.55310	+	3.30802i	0.149705	+	0.108767i
$926$		0			0
$927$	−26.3836	+	19.1688i	−0.866552	+	0.629587i
$928$		0			0
$929$	−6.13292	−	6.13292i	−0.201215	−	0.201215i	0.599306	−	0.800520i	$-0.295443\pi$
$929$	−6.13292	−	6.13292i	−0.201215	−	0.201215i	−0.800520	+	0.599306i	$0.795443\pi$
$930$		0			0
$931$	−0.586689	−	0.298933i	−0.0192280	−	0.00979713i
$932$		0			0
$933$	−12.8505	+	39.5499i	−0.420707	+	1.29480i
$934$		0			0
$935$	1.36672	+	0.444074i	0.0446965	+	0.0145228i
$936$		0			0
$937$	−4.33799	−	27.3890i	−0.141716	−	0.894759i	−0.951415	−	0.307913i	$-0.900370\pi$
$937$	−4.33799	−	27.3890i	−0.141716	−	0.894759i	0.809699	−	0.586846i	$-0.199630\pi$
$938$		0			0
$939$	−7.23819	−	22.2768i	−0.236209	−	0.726977i
$940$		0			0
$941$	15.4910	−	21.3216i	0.504993	−	0.695063i	−0.478072	−	0.878321i	$-0.658664\pi$
$941$	15.4910	−	21.3216i	0.504993	−	0.695063i	0.983065	+	0.183257i	$0.0586642\pi$
$942$		0			0
$943$	35.6364	−	32.1686i	1.16048	−	1.04755i
$944$		0			0
$945$	−1.15495	+	1.58965i	−0.0375706	+	0.0517115i
$946$		0			0
$947$	17.4125	+	53.5901i	0.565830	+	1.74144i	0.665474	+	0.746421i	$0.268230\pi$
$947$	17.4125	+	53.5901i	0.565830	+	1.74144i	−0.0996438	+	0.995023i	$0.531770\pi$
$948$		0			0
$949$	−1.79531	−	11.3351i	−0.0582782	−	0.367954i
$950$		0			0
$951$	26.1391	+	8.49312i	0.847619	+	0.275408i
$952$		0			0
$953$	−9.02900	+	27.7884i	−0.292478	+	0.900154i	0.691579	+	0.722301i	$0.256915\pi$
$953$	−9.02900	+	27.7884i	−0.292478	+	0.900154i	−0.984057	+	0.177854i	$0.943085\pi$
$954$		0			0
$955$	0.564766	+	0.287763i	0.0182754	+	0.00931178i
$956$		0			0
$957$	10.1019	+	10.1019i	0.326547	+	0.326547i
$958$		0			0
$959$	13.1823	−	9.57748i	0.425678	−	0.309273i
$960$		0			0
$961$	17.1931	+	12.4915i	0.554615	+	0.402952i
$962$		0			0
$963$	−41.9127	−	57.6879i	−1.35062	−	1.85897i
$964$		0			0
$965$	−0.752090	−	0.119119i	−0.0242106	−	0.00383459i
$966$		0			0
$967$	17.8304	−	9.08505i	0.573388	−	0.292156i	−0.143153	−	0.989701i	$-0.545724\pi$
$967$	17.8304	−	9.08505i	0.573388	−	0.292156i	0.716541	+	0.697545i	$0.245724\pi$
$968$		0			0
$969$	10.8317	−	21.2584i	0.347964	−	0.682918i
$970$		0			0
$971$	3.43652	−	0.544291i	0.110283	−	0.0174671i	−0.101049	−	0.994881i	$-0.532220\pi$
$971$	3.43652	−	0.544291i	0.110283	−	0.0174671i	0.211332	+	0.977414i	$0.432220\pi$
$972$		0			0
$973$	21.6342	+	42.4595i	0.693561	+	1.36119i
$974$		0			0
$975$		−	15.0106i		−	0.480725i
$976$		0			0
$977$	−0.933392	+	5.89321i	−0.0298619	+	0.188540i	−0.998110	−	0.0614501i	$-0.980428\pi$
$977$	−0.933392	+	5.89321i	−0.0298619	+	0.188540i	0.968248	+	0.249991i	$0.0804275\pi$
$978$		0			0
$979$	15.4983	−	5.03570i	0.495328	−	0.160942i
$980$		0			0
$981$	54.4879	−	54.4879i	1.73967	−	1.73967i
$982$		0			0
$983$	−42.8287			−1.36602			−0.683011	−	0.730408i	$-0.739330\pi$
$983$	−42.8287			−1.36602			−0.683011	+	0.730408i	$0.739330\pi$
$984$		0			0
$985$	−0.495816			−0.0157980
$986$		0			0
$987$	60.4270	−	60.4270i	1.92341	−	1.92341i
$988$		0			0
$989$	7.08074	−	2.30067i	0.225154	−	0.0731571i
$990$		0			0
$991$	−4.88595	+	30.8487i	−0.155207	+	0.979940i	0.779985	+	0.625799i	$0.215227\pi$
$991$	−4.88595	+	30.8487i	−0.155207	+	0.979940i	−0.935192	+	0.354141i	$0.884773\pi$
$992$		0			0
$993$			13.1463i			0.417184i
$994$		0			0
$995$	0.843059	+	1.65460i	0.0267268	+	0.0524542i
$996$		0			0
$997$	43.0807	−	6.82332i	1.36438	−	0.216097i	0.569065	−	0.822293i	$-0.307305\pi$
$997$	43.0807	−	6.82332i	1.36438	−	0.216097i	0.795315	+	0.606196i	$0.207305\pi$
$998$		0			0
$999$	−3.21200	+	6.30390i	−0.101623	+	0.199446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.bs.d.33.3		24
4.3	odd	2		41.2.g.a.33.3	yes	24
12.11	even	2		369.2.u.a.361.1		24
41.5	even	20	inner	656.2.bs.d.497.3		24
164.87	odd	20		41.2.g.a.5.3	✓	24
164.95	even	40		1681.2.a.m.1.22		24
164.151	even	40		1681.2.a.m.1.21		24
492.251	even	20		369.2.u.a.46.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.3	✓	24	164.87	odd	20
41.2.g.a.33.3	yes	24	4.3	odd	2
369.2.u.a.46.1		24	492.251	even	20
369.2.u.a.361.1		24	12.11	even	2
656.2.bs.d.33.3		24	1.1	even	1	trivial
656.2.bs.d.497.3		24	41.5	even	20	inner
1681.2.a.m.1.21		24	164.151	even	40
1681.2.a.m.1.22		24	164.95	even	40

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.bs (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.02366 - 2.02366i) q^{3} +(0.110420 - 0.0358775i) q^{5} +(0.422339 - 2.66654i) q^{7} -5.19040i q^{9} +O(q^{10})\)	\(q+(2.02366 - 2.02366i) q^{3} +(0.110420 - 0.0358775i) q^{5} +(0.422339 - 2.66654i) q^{7} -5.19040i q^{9} +(1.53663 + 3.01580i) q^{11} +(-1.03889 + 0.164544i) q^{13} +(0.150848 - 0.296056i) q^{15} +(3.25831 - 1.66019i) q^{17} +(2.25168 + 0.356630i) q^{19} +(-4.54151 - 6.25085i) q^{21} +(-6.06568 - 4.40698i) q^{23} +(-4.03418 + 2.93100i) q^{25} +(-4.43263 - 4.43263i) q^{27} +(1.31408 + 0.669558i) q^{29} +(0.964816 - 2.96940i) q^{31} +(9.21257 + 2.99335i) q^{33} +(-0.0490344 - 0.309591i) q^{35} +(-0.348766 - 1.07339i) q^{37} +(-1.76938 + 2.43534i) q^{39} +(-1.32339 + 6.26487i) q^{41} +(-0.583672 + 0.803355i) q^{43} +(-0.186219 - 0.573122i) q^{45} +(1.73020 + 10.9241i) q^{47} +(-0.274693 - 0.0892531i) q^{49} +(3.23405 - 9.95337i) q^{51} +(0.482987 + 0.246094i) q^{53} +(0.277873 + 0.277873i) q^{55} +(5.27833 - 3.83493i) q^{57} +(1.57246 + 1.14246i) q^{59} +(-5.95937 - 8.20238i) q^{61} +(-13.8404 - 2.19211i) q^{63} +(-0.108810 + 0.0554416i) q^{65} +(6.02949 - 11.8335i) q^{67} +(-21.1931 + 3.35666i) q^{69} +(4.28484 + 8.40947i) q^{71} +10.9108i q^{73} +(-2.23245 + 14.0952i) q^{75} +(8.69075 - 2.82380i) q^{77} +(-7.58864 + 7.58864i) q^{79} -2.36906 q^{81} +0.635212 q^{83} +(0.300218 - 0.300218i) q^{85} +(4.01421 - 1.30430i) q^{87} +(0.753161 - 4.75527i) q^{89} +2.83974i q^{91} +(-4.05659 - 7.96151i) q^{93} +(0.261424 - 0.0414055i) q^{95} +(-1.25412 + 2.46135i) q^{97} +(15.6532 - 7.97572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more